• Home
  • Download PDF
  • Order CD-ROM
  • Order in Print
Area of a Rhombus or Rhomboid
Area of an Ellipse

Engineering Aid 3 - Beginning Structural engineering guide book
Page Navigation
  7    8    9    10    11  12  13    14    15    16    17  
Area of a Circle Figure  1-11.-Trapezium. Figure 1-12.-Area of a circle. Stated  in  words, equal  to  one-half altitude. the  area  of  a  trapezoid  is the sum of its bases times its Area by Reducing to Triangles Figure  1-11  shows  you  how  you  can  determine the   area   of   a   trapezium,   or   of   any   polygon, by   reducing   to   triangles.   The   dotted   line connecting  A  and  C  divides  the  figure  into  the triangles  ABC  and  ACD.  The  area  of  the trapezium obviously equals the sum of the areas of these triangles. Figure  1-12  shows  how  you  could  cut  a disk  into  12  equal  sectors.  Each  of  these sectors  would  constitute  a  triangle,  except  for the slight curvature of the side that was originally a  segment  of  the  circumference  of  the  disk.  If this side is considered the base, then the altitude for  each  triangle  equals  the  radius  (r)  of  the original  disk.  The  area  of  each  triangle,  then, equals and the area of the original disk equals the sum of the areas of all the triangles. The sum of the areas of all the triangles, however, equals the sum of  all  the  b’s,  multiplied  by  r  and  divided  by  2. But   the   sum   of   all   the   b’s   equals   the circumference (c) of the original disk. Therefore, the  formula  for  the  area  of  a  circle  can  be expressed as However, the circumference of a circle equals the product  of  the  diameter  times  n  (Greek  letter, pronounced  “pi”).   n  is  equal  to  3.14159.  .  .  The diameter equals twice the radius; therefore, the circumference   equals   2rrr.  Substituting  2rrr for c  in  the  formula This is the most commonly used formula for the area of a circle. If we find the area  of the circle in  terms  of  circumference. Area of a Segment and a Sector A segment is a part of a circle bounded by a chord  and  its  arc,  as  shown  in  figure  1-13.  The formula  for  its  area  is where r = the radius and n = the central angle in degrees. 1-12







Western Governors University

Privacy Statement
Press Release
Contact

© Copyright Integrated Publishing, Inc.. All Rights Reserved. Design by Strategico.